Nilpotent Matrix A matrix A for which AP=0 where P is a positive integer is called nilpotent matrix. If P is the least positive integer for which AP=0 then A is said to be nilpotent of index P.
The spectrum of a nilpotent matrix consists solely of the eigenvalue zero. A nilpotent matrix ( N ) satisfies ( N^k = 0 ) for some positive integer ( k ), which implies that all its eigenvalues must be zero. Consequently, the only element in the spectrum (the set of eigenvalues) of a nilpotent matrix is ( {0} ). Thus, its spectral radius is also zero.
Involtary Matrix A square matrix A such that A2=I or (A+I)(A-I)=0, A is called involtary matrix.
The null matrix is also called the zero matrix. It is a matrix with 0 in all its entries.
can anyone give me an exact definition of payroll matrix................
Zero Matrix When all elements of a matrix are zero than the matrix is called zero matrix. Example: A=|0 0 0|
Identity or Unit Matrix If in the scaler matrix the value of k=1, the matrix is called the identity or unit matrix. It is denoted by I or U.
Lower-triangular Matrix A square matrix A whose elements aij=0 for i
Diagonal Matrix A square matrix A which is both uper-triangular and lower triangular is called a diagonal matrix. Diagonal matrix is denoted by D.
A square matrix A is idempotent if A^2 = A. It's really simple
Scaler Matrix If in the diagonal matrix D, a11=a22=a33=...=ann=k. Then D is called a scaler matrix.
from data structure
Uper-triangular Matrix A square matrix A whose elements aij=0 for i>j is called upper triangular matrix.